A TYPE I HALF LOGISTIC TOPP-LEONE INVERSE WEIBULL DISTRIBUTION: STATISTICAL PROPERTIES AND APPLICATIONS

Abstract

Researchers in the area of statistical distribution have made efforts on generalizing the existing
probability distributions to improve their modeling flexibility by adding extra parameters. In this
paper, a new continuous probability distribution called type I Half Logistic Topp-Leone Inverse
Weibull distribution with four parameters was derived. The nature of the new distribution with
the help of its mathematical and statistical properties such as quantile function, ordinary
moments, moment generating function and reliability were studied. The probability density
function of the minimum and maximum order statistics for the new distribution was also
obtained. A classical estimation of the unknown parameters of the model was done using the
technique of maximum likelihood estimation. Monte Carlo simulation study was carried out to
see the performance of maximum likelihood estimation method. The proposed model was
applied to two real datasets and the results showed that the new model provides a better fit than
the competing distributions considered.